Spectral drift and correction technique for hyperspectral imaging systems

ABSTRACT

A method for determining magnitude and direction of spectral channel drift for several consecutive spectral regions over a wide spectral range. According to the method of the present invention, in-field testing of a spectral filter sequentially irradiated by two blackbody sources is performed to generate a response function of the spectral filter. The response function is ensemble averaged to reduce any noise. Background radiance is then removed to produce a smoothed spectral transmittance function of the spectral filter. The first derivative function of the smoothed spectral transmittance function is determined. The first derivative function is separated into spectral band regions having +/− N pixels on either side of the function minima. The value of N is selected to optimize the detection algorithm sensitivity to change while extending the limit of spectral shift magnitude. The sum of the differences between the first derivative function and a reference spectral derivative function is determined. The difference result is applied to a look-up table to determine magnitude and direction of spectral drift for each of the separated spectral band regions. Use of the present invention can provide information on spectral distortion or spectral smile for 2-D focal plane arrays used for hyperspectral imaging.

[0001] This application claims the benefit of priority under 35 U.S.C. §119(e) to Appl. No. 60/221,270, filed Jul. 27, 2000, which isincorporated in its entirety herein by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates generally to the field of imagingsystems, and more particularly, to hyperspectral imaging systems. Theinvention further relates to a method for determining the magnitude anddirection of spectral drift in hyperspectral imaging systems.

[0004] 2. Related Art

[0005] All objects, such as soil, water, trees, vegetation, structures,metals, paints, fabrics, etc., create a unique spectral fingerprint. Theunique spectral fingerprint is a measure of the electromagnetic energythat is reflected or thermally generated from an object when the objectis being imaged. A sensor is used to determine the fingerprint. Thesensor measures the light reflected from the object or the thermallyradiated energy from the object, the majority of which registers inwavelengths or bands, invisible to humans.

[0006] Hyperspectral imaging refers to the imaging of an object over alarge number of discrete, contiguous spectral bands. Hyperspectralimaging produces images for which a spectral signature is associatedwith each spatial resolution element or pixel. A cross between imagingand spectroscopy, hyperspectral imaging is an outgrowth ofmulti-spectral imaging. Multi-spectral imagers take one measurement in awide portion of each major wavelength band. Unlike multi-spectralimagers, hyperspectral imagers measure energy in numerous narrow unitsof each band. The narrower bandwidths of a hyperspectral sensor are moresensitive to subtle variations in energy reflection or thermalgeneration. As a result, the hyperspectral signal is more detailed andcontains more specific information about the object imaged.

[0007] A hyperspectral imager can see what cannot be seen by the humaneye. Hyperspectral imaging, combined with image processing and analysis,can identify materials, classify features, identify trends, etc.Hyperspectral imaging can be used for, but is not limited to, medicalphoto-diagnosis, chemical detection, cloud tracking, earth resources,remote sensing of pollutants and other compounds in the atmosphere,soil, and waters, remote sensing of land and oceans, and targetdetection and recognition.

[0008] Hyperspectral imaging systems require precise control andidentification of spectral channel assignments during image datarecording. For precise radiometric and spectral detection algorithms tobe effective it is essential to maintain spectral channel calibrationduring operation. Knowledge of the spectral bands during imageprocessing allows utilization of a wide range of algorithms to determinematerial identification based upon spectral signature information.

[0009] Identification of the spectral channel assignments during imagingoperations is required to determine the amount of spectral drift whichcan occur during mission environments and provide the informationnecessary to correctly reassign the spectral channels to thehyperspectral imagery. What is needed is a system and method fordetecting spectral drift. What is further needed is a system and methodfor determining the amount as well as the direction of spectral drift.

SUMMARY OF THE INVENTION

[0010] The present invention is a method for detecting magnitude anddirection of spectral drift in a hyperspectral imaging system. Moreparticularly, the present invention is a method for determiningmagnitude and direction of spectral channel drift for several contiguousspectral regions over a wide spectral range in hyperspectral imagingsystems. According to the method of the present invention, in-fieldtesting with a spectral filter sequentially irradiated by two blackbodysources is performed to generate a response function of the spectralfilter. The response function is ensemble averaged to reduce any noise.Background radiance is then removed to produce a smoothed spectraltransmittance function of the spectral filter. The first derivativefunction of the spectral transmittance function is then determined. Thefirst derivative function is partitioned into spectral band regionshaving +/− N pixels on either side of the function minima. The value ofN is selected to optimize the detection algorithm sensitivity to changewhile extending the limit of spectral shift magnitude. The sum of thedifferences between the first derivative function and a referencespectral derivative function is determined. The difference result isapplied to a look-up table to determine magnitude and direction ofspectral drift for each of the partitioned spectral band regions.

[0011] Use of the present invention can provide information on spectraldistortion or spectral smile for 2-D focal plane arrays used forhyperspectral imaging.

[0012] Further features and advantages of the invention, as well as thestructure and operation of various embodiments of the invention, aredescribed in detail below with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE FIGURES

[0013] The accompanying drawings, which are incorporated herein and formpart of the specification, illustrate the present invention and,together with the description, further serve to explain the principlesof the invention and to enable a person skilled in the pertinent art tomake and use the invention.

[0014]FIG. 1A is an exemplary block diagram illustrating a hyperspectralimaging system according to an embodiment of the present invention.

[0015]FIG. 1B is an exemplary block diagram illustrating a hyperspectralimaging system having a spectral calibration subsystem with twoblackbody sources and a spectral calibration filter assembly accordingto an embodiment of the present invention.

[0016]FIG. 1C is a high level flow chart illustrating a method fordetermining magnitude and direction of spectral channel drift for ahyperspectral imaging system according to an embodiment of the presentinvention.

[0017]FIG. 2 is a flow diagram describing a method for generatingreference signals during pre-field testing.

[0018]FIG. 3 is a graph illustrating exemplary spectral channelcalibration filter measurements for an SRM1921a Polystyrene Filterutilizing two blackbody sources.

[0019]FIG. 4 is a graph of an exemplary spectral channel filtertransmittance function.

[0020]FIG. 5 is a flow diagram describing a method for generating alook-up table for the detection of spectral drift in hyperspectralimaging systems.

[0021]FIG. 6 is a graph illustrating an exemplary spectral channel driftlook-up table for each filter band of the SRM1921a polystyrene filter.

[0022]FIG. 7 is a flow diagram describing a method for generatingmeasured signals during in-field testing of the calibration filter.

[0023]FIG. 8 is a graph illustrating an exemplary first derivativeresponse of the measured calibration filter transmittance.

[0024]FIG. 9 is a diagram illustrating an exemplary computer system.

[0025]FIG. 10 is a diagram illustrating an exemplary 2-D focal planearray used for hyperspectral imaging.

[0026] The features, objects, and advantages of the present inventionwill become more apparent from the detailed description set forth belowwhen taken in conjunction with the drawings in which like referencecharacters identify corresponding elements throughout. In the drawings,like reference numbers generally indicate identical, functionallysimilar, and/or structurally similar elements. The drawings in which anelement first appears is indicated by the leftmost digit(s) in thecorresponding reference number.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0027] While the present invention is described herein with reference toillustrative embodiments for particular applications, it should beunderstood that the invention is not limited thereto. Those skilled inthe art with access to the teachings provided herein will recognizeadditional modifications, applications, and embodiments within the scopethereof and additional fields in which the present invention would be ofsignificant utility.

[0028] Overview

[0029] The present invention is a method for detecting magnitude anddirection of spectral drift in a hyperspectral imaging system. Themethod of the present invention is designed to recalibrate the spectralchannels of the hyperspectral imaging system while in field.Quantification of spectral channel drift during imaging operations isrequired to provide the information necessary to correctly recalibratethe spectral channels to a hyperspectral image cube data. In order tomeet the needs of spectral channel drift detection and provide adequateinformation for channel correction, the methods described herein aredesigned to detect sub-pixel spectral drift, the magnitude of thespectral drift, and the direction of the spectral drift for spectralchannel assignments. Sampling of a wide spectral range of thehyperspectral imaging system over several contiguous spectral regionsallows non-linear detection of spectral drift and provides theinformation required for correction.

[0030] The methods described herein can be applied to any operationalhyperspectral imaging system where the operational condition of “field”or “infield” is equivalently interpreted as, but is not limited to,“in-flight”, “shipboard”, “ground-based” or “space-borne”. The methodsdescribed herein apply to all environments.

[0031] The present invention is described for long wave spectral regionsin which radiation is thermally generated. In other words, the signatureof an imaged object is a function of the temperature of the object andthe spectral emissivity. Emissivity is the ratio of energy radiated byan object to the energy radiated by a blackbody at the same temperature.Emissivity is a function of wavelength and temperature. An idealblackbody source is a material that absorbs all of the incidentradiation, reflecting none. Blackbody sources are thermal sources withemissivity characteristics of approximately one. Blackbody sourcesfollow Max Planck's blackbody equations in terms of optical spectralradiance. Planck's blackbody equations are well known to persons skilledin the relevant art(s). One skilled in the relevant art(s) would alsoknow that the present invention is not limited to long wave spectralregions in which radiation is thermally generated, but is alsoapplicable to other spectral regions, such as visible through mid wave,in which radiation is generated from solar energy.

[0032] In order for radiometric and spectral detection algorithms to beeffective, spectral channel calibration must be maintained duringhyperspectral image data recording. Spectral drift may occur duringmission environments, making it necessary to reassign the spectralchannels to the hyperspectral imagery. The present invention samples awide spectral range of the hyperspectral image over several spectralregions for non-linear detection of spectral drift. The invention alsoprovides the information required for correction.

[0033] Prior to describing the invention in detail, a brief descriptionof a filter used to calibrate the hyperspectral system is discussed. Theinvention uses a SRM1921a Polystyrene filter, provided by NIST (NationalInstitutes for Science and Technology), as the calibration filter. TheSRM1921a calibration filter provides a calibrated spectrum that is usedas a reference. The SRM1921a calibration filter has at least seven (7)spectral band regions over a spectral range of 8 to 11 μm. The SRM1921acalibration filter also provides additional bands over the spectralrange of 3.2 to 18 μm. Although the present invention uses an SRM1921apolystyrene filter as the calibration filter, one skilled in therelevant art(s) would know that other filters having multiple spectralband regions over a desired spectral range maybe used as the calibrationfilter without departing from the scope of the present invention.

[0034]FIG. 1A is a block diagram illustrating an exemplary hyperspectralimaging system 120 according to an embodiment of the present invention.Hyperspectral imaging system 120 may be installed in an air-bornesystem, a space-borne system, or a ground-based system. Hyperspectralimaging system 120 comprises an optical train 122, a disperser 124, afocal plane detector array (FPA) 126, a processor 128, and a controller130. Optical train 122 is coupled to disperser 124. Disperser 124 iscoupled to FPA 126. FPA 126 is coupled to processor 128. Processor 128is coupled to controller 130 via a bi-directional data bus. Controller130 is also coupled to optical train 122 and FPA 126. Data link 132 is abi-directional data link that also couples to controller 130. Data link132 comprises a receiver and a transmitter for connecting data link 132to an image and data processing station contained in one or both of acontrol station 134 or an in-field platform 136. In-field platform 136may be an air-borne platform, a ground-based platform, or a space-borneplatform.

[0035] The components (122, 124, 126, 128, and 130) of hyperspectralimaging system 120 work together to collect, detect, and processinfrared radiation, represented by the greek symbol λ (lambda). Infraredradiation (λ) is received by optical train 122. Optical train 122comprises a steerable group of optical elements (not shown) whichcollect and focus the infrared radiation (λ). Controller 130 provideselectromechanical control signals to enable optical train 122 to collectand focus the infrared radiation (λ). The infrared radiation (λ)collected by optical train 122 is sent to disperser 124. Disperser 124may include a diffraction grating assembly, a compensated prismassembly, or an electro-optic device such as a Fabry-Perot etalon oracousto-optic assembly. Disperser 124 separates the received infraredradiation (λ) into spectral components and disperses the spectralcomponents, as shown by arrows 125. The output of disperser 124 isincident upon FPA 126. FPA 126 is a focal plane detector array of pixelsthat sense each of the spectral bands of radiation produced by disperser124 and generate a corresponding output signal. Controller 130 providescontrol lines for activating and directing the operation of the arrayfor FPA 126. The corresponding output signal from FPA 126 is sent toprocessor 128 for processing.

[0036] During spectral channel calibration, the calibration filter isinserted into an optical path of the hyperspectral imaging system. Thisusually takes place before and after imaging sequences. FIG. 1B is anillustration of hyperspectral imaging system 120 displaying a spectralcalibration subsystem 140 contained within optical train 122. Spectralcalibration subsystem 140 is shown in phantom inside optical train 122to indicate that subsystem 140 may be inserted and removed from opticaltrain 122 depending upon the type of operation (i.e., calibration) beingperformed by hyperspectral imaging system 120. Spectral calibrationsubsystem 140 comprises two blackbody sources, BB₁(t₁) and BB₂(t₂), aspectral calibration filter 142 (such as the calibration filterdescribed above), and a flip mirror 144. The two blackbody sourcesBB₁(t₁) and BB₂(t₂) are two separate blackbody sources that arepre-stabilized to two separate desired temperatures. Alternatively, oneblackbody source could be used at two separate temperatures. Blackbodysources BB₁(t₁) and BB₂(t₂) are normally placed in an off-axis positionrelative to optical train 122. During spectral calibration operation,blackbody sources BB₁(t₁) and BB₂(t₂) are placed sequentially within thepath of optical train 122 using flip mirror 124. Spectral calibrationfilter 142 may also be placed in the path of optical train 122, with orwithout blackbody sources BB₁(t₁) and BB₂(t₂). Spectral calibrationoperations are described in detail below.

[0037]FIG. 1C is a high level flow diagram describing a method fordetermining magnitude and direction of spectral channel drift for thehyperspectral imaging system. The process begins with step 102, andproceeds immediately to step 104.

[0038] In step 104, reference signals are generated during pre-fieldtesting of calibration filter 142. Pre-field testing involves measuringthe spectrum of calibration filter 142 using two blackbody temperatures.Pre-field tests are performed in a controlled laboratory environment.The generation of reference signals is described below in greater detailwith reference to FIG. 2.

[0039] In step 106, a look-up table is generated using the referencesignals generated from step 104. The look-up table provides magnitudeand direction of pixel drift for each spectral band region ofcalibration filter 142. The generation of the look-up table is describedbelow with reference to FIG. 5.

[0040] In step 108, measured signals of calibration filter 142 aregenerated during in-field testing. In-field testing is performed duringairborne, ground-based, or ship-borne missions, and involves measuringthe spectrum of calibration filter 142 using two blackbody temperatures.The generation of measured signals is described below with reference toFIG. 7.

[0041] In step 110, a sum of the differences analysis between themeasured signals and the reference signals is performed. The sum of thedifferences analysis results in a value that is applied to the look-uptable generated in step 106.

[0042] In step 112, the difference analysis result is applied to thelook-up table to determine both the magnitude of pixel drift and thedirection of pixel drift in the +/− spectral direction for thecorresponding spectral band region of calibration filter 142. Spectralchannel assignments for each pixel in each band of calibration filter142 can then be corrected using the results from the look-up table. Theprocess ends at step 114.

[0043] Pre-Field Measurements and Analysis

[0044]FIG. 2 is a flow diagram describing a method 200 for generatingreference signals during pre-field testing. The process begins with step202, and proceeds immediately to step 204.

[0045] In step 204, the reference spectrum for each pixel assignment ofcalibration filter 142 is measured. The reference spectrum is measuredwith calibration filter 142 being irradiated by two blackbodytemperatures BB₁(t₁) and BB₂(t₂), selected sequentially using flipmirror 144. Actuation of flip mirror 144 in a first position withcalibration filter 142 in the optical path provides the correct spectralflux distribution for a blackbody source at temperature t₁ (BB₁(t₁)).The response reference spectrum for each pixel assignment whencalibration filter 142 is irradiated by a reference blackbody source attemperature t₁(BB₁(t₁)) is

RPCF_(I)(t₁)  (1)

[0046] where: I represents a pixel assignment for each spectral band incalibration filter 142. Each pixel assignment is defined in the spectraldomain and, for the present example, each pixel has a finite spectralwidth of 16.67 mm and I=1, . . . , 185. Actuation of flip mirror 144 toa second position with calibration filter 142 in the optical pathprovides the correct spectral flux distribution for a blackbody sourceat temperature t₂ (BB₂(t₂)). The response reference spectrum for eachpixel assignment when calibration filter 142 is irradiated by areference blackbody source at temperature t₂ (BB₂(t₂)) is

RPCF_(I)(t₂)  (2)

[0047] Measurements are also obtained for the reference blackbody sourceat temperatures t₁ and t₂ without calibration filter 142. Flip mirror144 is actuated to the first position without calibration filter 142 forthe blackbody source at temperature t₁(BB₁(t₁)). The response for thereference blackbody source at temperature t₁ is

RPBB_(I)(t₁)  (3)

[0048] Flip mirror 144 is actuated to the second position withoutcalibration filter 142 for the blackbody source at temperaturet₂(BB₂(t₂)). The response for the reference blackbody source attemperature t₂ is

RPBB_(I)(t₂)  (4)

[0049] Several frames of data are captured during the measurement of thereference spectrum pixel assignment for ensemble averaging. For example,in one embodiment, 128 consecutive spectral frames for RPCF_(I)(t₁),RPCF_(I)(t₂), RPBB_(I)(t₁), and RPBB_(I)(t₂) are captured and ensembleaveraged. The corresponding ensemble averaged functions areERPCF_(I)(t₁), ERPCF_(I)(t₂), ERPBB_(I)(t₁), and ERPBB_(I)(t₂),respectively. Ensemble averaging reduces measurement system noise thatmay have resulted.

[0050] In step 206, background radiance due to the filter and blackbodyspectral emittance is removed to produce a smoothed spectraltransmittance profile of calibration filter 142. Background radiance isremoved using a spectrum difference function and a blackbody differencefunction. The filter spectrum difference function subtracts the responsereference spectrum for the two blackbody temperatures. The filterspectrum difference function is

DRPCF _(I) =ERPCF _(I)(t ₁)−ERPCF _(I)(t ₂)  (5)

[0051] The blackbody difference function is the difference between theresponses for the reference blackbody sources at the two temperatures t₁and t₂. The reference blackbody difference function is

RBBDF _(I) =ERPBB _(I)(t ₁)−ERPBB _(I)(t ₂)  (6)

[0052]FIG. 3 is a graph 300 illustrating exemplary spectral channelcalibration filter measurements for an SRM1921a Polystyrene Filterutilizing two blackbody sources (BB₁(t₁) and BB₂(t₂)). A y-axis 302 ofgraph 300 represents spectral radiance (flicks) and an x-axis 304represents wavelength (μm). A first plot 306 represents the referencespectrum of calibration filter 142 irradiated by the reference blackbodysource at temperature t₁ (BB₁(t₁)). Temperature t₁ is 300° Kelvin (K). Asecond plot 308 represents the reference spectrum of calibration filter142 irradiated by the reference blackbody source at temperaturet₂(BB₂(t₂)). Temperature t₂ is 280° K. A third plot 310 represents thespectrum difference function for the reference spectrum of calibrationfilter 142 irradiated by the reference blackbodies at temperatures t₁and t₂ (BB₁(t₁) and BB₂(t₂)).

[0053] Returning to FIG. 2, in step 208, the reference spectraltransmittance function for calibration filter 142 is determined. Thereference spectral transmittance function is equal to the spectrumdifference function divided by the blackbody difference function.

RP _(I)(ref)=DRPCF _(I) /RBBDF _(I)  (7)

[0054] Calibration filter data, supplied by NIST, for the SRM1921afilter is compared with the reference spectral transmittance functionRP_(I)(ref). Using the NIST supplied calibration filter data, wavelengthbands are assigned to each of the spectral pixel channels. FIG. 4 is agraph 400 of an exemplary spectral channel filter transmittance functionfor the SRM1921a Polystyrene filter. A y-axis 402 of graph 400 displaysa spectral transmittance and an x-axis 404 displays a wavelength (μm).As shown in graph 400, calibration filter 142 provides a stable spectraltransmittance band profile 406 over an exemplary range of 8 to 11 μm.Calibration filter 142 displays multiple spectral transmittance bands408-420 over the required spectral range. Each transmittance band408-420 has a spectral transmittance bandwidth of at least 50 nm at FWHM(full width half maximum). The spectral transmittance bands 408-420 areinsensitive to thermal drift over a 0° to 50° C. ambient temperature.

[0055] Returning to FIG. 2, in step 210, a first derivative function foreach reference pixel assignment of the spectral transmittance functionis determined. The discrete first derivative function is

dRP _(I) =ΔRP _(I)/Δλ_(I)=(RP _(I+1) −RP _(I))/(λ_(I+1)−λ_(I))  (8)

[0056] where: ΔRP_(I) is the change in the reference spectraltransmittance function between pixels; and Δλ_(I) is the change inwavelength between pixels.

[0057] The first derivative function, dRP_(I), is then normalized. Thefirst step in the normalization process eliminates all negative valuesof the first derivative function dRP_(I) by adding a positive value toeach discrete value of the first derivative function (shown below asdRP_(I)positive)). The magnitude of the positive value is equal to themagnitude of the greatest negative value of the first derivativefunction, dRP_(I). The normalized value of the first derivativefunction, dRP_(I)normalized), is obtained by dividing the resultantdiscrete values of dRP_(I)(positive) by the maximum positive value ofdRP_(I)(positive) to enable the greatest value of the normalized firstderivative function to be equal to one (1).

dRP _(I)(positive)=(dRP _(I) +MAG(greatest negative value(dRP_(I))))  (9)

dRP _(I)(normalized)=dRP _(I)(positive)/(maximum value (dRP_(I)(positive))  (10)

[0058] To implement the full sensitivity to spectral drift required forhyperspectral imaging applications, the normalized first derivativefunction is further sampled. Seven localized minima for the normalizedfirst derivative function dRP_(I)(normalized) are determined. The sevenlocalized minima are based upon the SRM1921a filter function. The sevenlocalized minima are labeled with increasing values from 1 to 7, withthe label 1 being assigned to the shortest wavelength and the label 7being assigned to the longest wavelength. A record length for each ofthe seven localized minima of the normalized first derivative function(dRP_(I)normalized)) is truncated. Truncation of the record length isperformed using seven segments. Each segment is centered upon the pixellocation of the localized minima. Each segment length is set equal to+/− N(Z)+1, where N is equal to the number of pixels on either side ofthe localized minima and Z is referred to as the spectral band zone foreach segment (1, . . . , 7) of the normalized first derivative function(dRP_(I)(normalized)).

[0059] In step 212, the normalized reference first derivative functionis separated into spectral band regions and truncated with +/− N pixelson either side of the localized minima. The value of N is selected tooptimize the detection algorithm sensitivity to change while extendingthe limit of spectral shift magnitude. The spectral band per pixel isdefined by the optical geometry of system focal length and detectorsize, along with the spectral dispersion rate design of thehyperspectral imaging system. In one embodiment, N=+/−10 pixels for eachof seven zones, where one pixel is equivalent to 16.67 nm.

[0060] In yet another embodiment, the value of N may change according tothe spectral band zone. In an embodiment where a certain value of N isfound to be sensitive for some of the zones, yet insensitive for otherzones, the value of N may be changed for those zones found to beinsensitive. For example, in one embodiment, a value of N=+/−10 pixelsshows good sensitivity for zones 1, 3, 4, 5, and 7, but not for zones 2and 6. Thus, to provide good sensitivity for all seven zones, N is setequal to +/−10 for zones 1, 3, 4, 5, and 7, and N is less than 7 forzones 2 and 6. One skilled in the relevant art(s) would know that othervalues of N could be used based on the parameters of the hyperspectralimaging system without departing from the scope of the presentinvention.

[0061] In step 214, the reference spectral transmittance function andthe first derivative functions of the reference spectral transmittancefunction are stored as reference signals. The process ends at step 216.

[0062] Generation of the Look-up Table

[0063]FIG. 5 is a flow diagram describing a method for generating alook-up table for the detection of spectral drift in hyperspectralimaging systems. The look-up table is generated using the firstderivative of the reference spectral transmittance function for eachspectral band of calibration filter 142. The process begins with step502, and proceeds immediately to step 504.

[0064] In step 504, the process begins for each spectral band. Forexample, the SRM1921a polystyrene filter has seven prominent bands inwhich a localized minima results (see FIG. 4). This requires the processbeginning with step 504 to be repeated seven times.

[0065] In step 506, the process begins for each predefined pixel shiftwithin each filter band. For example, if the look-up table providesresults for pixel shifts of ½, the process will be repeated for every ½pixel shift within the filter band.

[0066] In step 508, the first derivative of the reference spectraltransmittance function is shifted by a known pixel amount. The firstderivative of the reference spectral transmittance function is shiftedin both a positive and a negative direction in order to obtain magnitudeand direction of spectral drift.

[0067] In step 510, a difference value is determined by taking thedifference between the shifted first derivative function and thenon-shifted first derivative function.

[0068] In step 512, the difference value along with the known pixelshift are stored in the look-up table. The process returns to step 506to complete the look-up table for the current filter band by recursivelyrepeating steps 506 to 512. Upon completion of the look-up table for thecurrent filter band, the process returns to step 504 to begin theprocess for the next filter band by recursively repeating steps 504 to512. Upon completion of the last filter band, the process proceeds tostep 514.

[0069] In step 514, the look-up table is stored in memory. The processends at step 516.

[0070]FIG. 6 is a graph 600 illustrating the function plots of anexemplary spectral channel drift look-up table for each of the definedfilter bands of the SRM1921a polystyrene calibration filter. A y-axis602 displays the magnitude of the look-up table or the difference valueand an x-axis 604 displays the number of pixel drifts. The number ofpixel drifts is displayed from −5 to +5 in increments of ½. A first plot606 displays the difference value for a given pixel drift for filterband 408. A second plot 608 displays the difference value for a givenpixel drift for filter band 410. A third plot 610 displays thedifference value for a given pixel drift for filter band 412. A fourthplot 612 displays the difference value for a given pixel drift forfilter band 414. A fifth plot 614 displays the difference value for agiven pixel drift for filter band 416. A sixth plot 616 displays thedifference value for a given pixel drift for filter band 418. And aseventh plot 618 displays the difference value for a given pixel driftfor filter band 420.

[0071] In-Field Measurements and Analysis

[0072]FIG. 7 is a flow diagram describing a method 700 for generatingmeasured signals during in-field testing of calibration filter 142.Method 700 is very similar to method 200, except that the measuredsignals are generated from in-field measurements of calibration filter142. The process begins with step 702, and proceeds immediately to step704.

[0073] In step 704, the in-field spectrum for each pixel assignment ofcalibration filter 142 is measured. The in-field spectrum is measuredwith calibration filter 142 being irradiated by two blackbodytemperatures BB₁(t₁) and BB₂(t₂), selected sequentially using flipmirror 144. Flip mirror 144 is an actual mirror that flips into theoptical path of the hyperspectral imaging system during calibration toallow the focal plane of the system to view the blackbodies (BB₁(t₁) andBB₂(t₂)) and spectral filter 142 in the optical path. Flip mirror 144flips out of the optical path during actual imaging. The responsespectrum for each pixel assignment when calibration filter 142 isirradiated by an onboard blackbody source at temperature t₁ (BB₁(t₁)) is

MPCF_(I)(t₁)  (11)

[0074] where: I represents a pixel assignment for each spectral band408-420 of calibration filter 142. As previously stated, for the presentexample, each pixel has a finite spectral width of 16.67 nm and I=1, . .. , 185. The response spectrum for each pixel assignment whencalibration filter 142 is irradiated by the onboard blackbody source attemperature t₂ (BB₂(t₂)) is

MPCF_(I)(t₂)  (12)

[0075] Measurements are also obtained for the onboard blackbody attemperature t₁ and t₂ (BB₁(t₁) and BB₂(t₂)) without calibration filter142. The response for the onboard blackbody source at temperature t₁(BB₁(t₁)) is

MPBB_(I)(t₁)  (13)

[0076] The response for the onboard blackbody source at temperature t₂(BB₂(t₂)) is

MPBB_(I)(t₂)  (14)

[0077] Several frames of data are collected at equivalent frame times.For example, 128 frames of data are collected for the onboard blackbodysource at t₁ BB₁(t₁)) and then 128 frames of data are collected for theonboard blackbody source at t₂ (BB₂(t₂)). The filter dwell time for 128frames is equal to 1.1×128×frame time. The frame time range can varyfrom 2.5 ms to 9 ms, depending on the flight parameters of altitude,ground speed, and path phenomenology. Although values for the number offrames, frame time, and filter dwell time are given as 128, 2.5 to 9 ms,and 1.1×128×frame time, respectively, one skilled in the relevant art(s)would know that other values for the number of frames, frame times, andfilter dwell time may be used without departing from the scope of thepresent invention. The frame data is ensemble averaged for eachblackbody or blackbody and filter combination. For example, in oneembodiment, 128 consecutive spectral frames for MPCF_(I)(t₁),MPCF_(I)(t₂), MPBB_(I)(t₁), and MPBB_(I)(t₂) are captured and ensembleaveraged. The corresponding ensemble averaged functions areEMPCF_(I)(t₁), EMPCF_(I)(t₂), EMPBB_(I)(t₁), and EMPBB_(I)(t₂). Ensembleaveraging reduces any noise that may have resulted from the measurementsystem.

[0078] In step 706, background radiance is removed to produce a smoothedspectral transmittance profile of calibration filter 142. Backgroundradiance is removed using a spectral difference function and a blackbodydifference function. The use of two blackbody temperatures enables thesubtraction of the spectral radiance of the filter, thereby resulting ina pure transmittance function. The spectral difference function is

DMPCF _(I) =EMPCF _(I)(t ₁)−EMPCF _(I)(t₂)  (15)

[0079] The blackbody difference function is the difference between theresponses for the onboard blackbody at the two temperatures, t₁ and t₂.The blackbody difference function is

MBBDF _(I) =EMPBB _(I)(t ₁)−EMPBB _(I)(t ₂)  (16)

[0080] In step 708, the onboard measured transmittance function forcalibration filter 142 for each pixel assignment is determined. Theonboard measured transmittance function is equal to the measuredspectral difference function divided by the measured blackbodydifference function.

MP _(I)(ref)=DMPCF _(I) /MBBDF _(I)  (17)

[0081] In step 710, a first derivative function for the measuredtransmittance function for each pixel assignment is determined. Thediscrete first derivative function is

dMP _(I) =ΔMP _(I)/Δλ_(I)=(MP _(I+1) −MP _(I)/(λ_(I+1)−λ_(I))  (18)

[0082] where: ΔMP_(I) is the change in the measured transmittancefunction between pixels and Δλ_(I) is the change in wavelength betweenpixels. The first derivation function is used to create anon-symmetrical profile function while maintaining precise absorptionband information.

[0083] The first derivative function (dMP_(I)) is then normalized byfirst adding a positive value to each discrete value to eliminate allnegative values of the first derivative function (shown below inequation (19) as dMP_(I)(positive). The magnitude of the positive valueis equal to the magnitude of the greatest negative value of the firstderivative function, DMP_(I). Then the normalized first derivativefunction, dMP_(I)(normalized), is obtained by dividing the resultantdiscrete values of dMP_(I)(positive) by the maximum positive value ofdMP_(I)(positive) as shown in equation (20).

dMPI(positive)=(dMP _(I) +MAG(greatest negative value(dMP _(I))))  (19)

dMP _(I)(normalized)=dMP _(I)(positive)/(maximum value (dMP_(I)(positive))  (20)

[0084] The normalized first derivative function is further sampled toimplement the full sensitivity to spectral drift required forhyperspectral imaging applications. In one embodiment, seven localizedminima for the normalized first derivative function are determined. Theseven localized minima are based upon the SRM1921a filter function. Theseven localized minima are labeled with increasing values from 1 to 7,with the label 1 being assigned to the shortest wavelength and the label7 being assigned to the longest wavelength. A record length for each ofthe seven localized minima of the normalized first derivative functionis truncated. Truncation of the record length is performed using sevensegments. Each segment is centered upon the pixel location of thelocalized minima. Each segment is set equal to +/−N(Z)+1, where N isequal to the number of pixels on either side of the localized minima andZ is referred to as the spectral band zone for each segment (1,..., 7)of the normalized first derivative function (dMP_(I)(normalized)).

[0085] In step 712, the measured first derivative function ispartitioned into spectral band regions and truncated with +/− N pixelson either side of the localized minima. The value of N is selected tooptimize the detection algorithm sensitivity to change while extendingthe limit of spectral shift magnitude. The spectral band per pixel isdefined by the optical geometry of system focal length and detectorsize, along with the spectral dispersion rate design of thehyperspectral imaging system. In one embodiment, N=+/−10 pixels for allseven zones, where one pixel is equivalent to 16.67 nm.

[0086] In another embodiment, the value of N may change with respect tothe spectral band zone. For example, in an embodiment where a certainvalue of N is found to be sensitive for some of the zones, yetinsensitive for other zones, the value of N may be changed for thosezones found to be insensitive to that value of N. One skilled in therelevant art(s) would know that other spectral band per pixel sizescould be used based on the parameters of the hyperspectral imagingsystem without departing from the scope of the present invention.

[0087] In step 714, the measured spectral transmittance function foreach pixel assignment and the first derivative functions of the measuredspectral transmittance function are stored as measured signals. Theprocess ends at step 716.

[0088]FIG. 8 is a graph 800 illustrating an exemplary first derivativeresponse of the measured calibration filter transmittance function.Graph 800 comprises a y-axis 802 displaying a normalized firstderivative response of the measured calibration filter transmittance, anx-axis 804 displaying wavelength (μm), and a plot of the normalizedfirst derivative response of the measured calibration filtertransmittance function 806. Plot 806 identifies each filter band 808-820of calibration filter 142. Note that the filter bands are centeredaround localized minimas of the spectrum.

[0089] Determining Magnitude and Direction of Spectral Drift

[0090] Returning to FIG. 1, step 110, the difference analysis betweenthe measured signals and the reference signals involves thedetermination of a pixel shift magnitude value, PSM_(B)(k), which is thesum of the differences between the measured first derivative functionand the reference first derivative function from a starting point pixelnumber to an ending point pixel number.

PSM _(B)(k)=Σ(dMP _(I)(k)−dRP _(I)(k)), from I=n to n+20  (21)

[0091] where: n=starting point pixel number for band k; n+20 =endingpoint pixel number for band k; and k=1, 2, 3, . . . , 7 for each of theseven significant band zones of calibration filter 142. Spectral shiftsare detected to within ½ pixel. Once the pixel shift magnitude value isdetermined, the process proceeds to step 112.

[0092] In step 112, the pixel shift magnitude value is the differencevalue that is applied to the look-up table to determine pixel driftmagnitude and direction. For example, referring back to FIG. 6, if thepixel shift magnitude or difference value is 0.7 for band 1, the pixeldrift would be −5.

[0093] The pixel drift magnitude and direction are used to generate newspectral channel assignments for each pixel of the corresponding bandfor correcting the pixel drift. Interpolation methods are used todetermine the in-between values.

[0094] Although the present invention has been described using theSRM1921a filter, other filters having more or less filter bands anddifferent wavelengths may be implemented without departing from thescope of the present invention.

[0095] Other Features of the Invention

[0096] The present invention also provides the ability to measure andcorrect magnitude and direction of spectral drift for different spatialpixels in a 2-D focal plane array. The invention provides information onspectral distortion and spectral smile for 2-D focal plane arrays. FIG.10 is a diagram illustrating an exemplary 2-D focal plane array 1000used for hyperspectral imaging. 2-D focal plane array 1000 is comprisedof columns 1002 and rows 1004 of data. Each column 1002 representsspectral pixels with a spectrum band assignment for each pixel j=1through L, where L=185. Each row 1004 represents spectral data for asingle spectral channel for all of the spatial pixels i=1 through M.

[0097] The optical system geometry can distort the magnitude anddirection of the spectral drift. The methods of the present invention,described herein, measure and correct the magnitude and direction ofspectral drift for different spatial pixels 1 through M, representingcolumns 1002 of the 2-D array 1000, to correct for such distortion.

[0098] Implementation of the Present Invention

[0099] The present invention may be implemented using hardware,software, or a combination thereof and may be implemented in one or morecomputer systems or other processing systems. In fact, in oneembodiment, the invention is directed toward one or more computersystems capable of carrying out the functionality described herein. Anexample implementation of a computer system 900 is shown in FIG. 9.Various embodiments are described in terms of this exemplary computersystem 900. After reading this description, it will be apparent to aperson skilled in the relevant art how to implement the invention usingother computer systems and/or computer architectures. The computersystem 900 includes one or more processors, such as processor 903. Theprocessor 903 is connected to a communication bus 902.

[0100] Computer system 900 also includes a main memory 905, preferablyrandom access memory (RAM), and may also include a secondary memory 910.The secondary memory 910 may include, for example, a hard disk drive 912and/or a removable storage drive 914, representing a floppy disk drive,a magnetic tape drive, an optical disk drive, etc. The removable storagedrive 914 reads from and/or writes to a removable storage unit 918 in awell-known manner. Removable storage unit 918, represents a floppy disk,magnetic tape, optical disk, etc., which is read by and written to byremovable storage drive 914. As will be appreciated, the removablestorage unit 918 includes a computer usable storage medium having storedtherein computer software and/or data.

[0101] In alternative embodiments, secondary memory 910 may includeother similar means for allowing computer programs or other instructionsto be loaded into computer system 900. Such means may include, forexample, a removable storage unit 922 and an interface 920. Examples ofsuch may include a program cartridge and cartridge interface (such asthat found in video game devices), a removable memory chip (such as anEPROM, or PROM) and associated socket, and other removable storage units922 and interfaces 920 which allow software and data to be transferredfrom the removable storage unit 922 to computer system 900.

[0102] Computer system 900 may also include a communications interface924. Communications interface 924 allows software and data to betransferred between computer system 900 and external devices. Examplesof communications interface 924 may include a modem, a network interface(such as an Ethernet card), a communications port, a PCMCIA slot andcard, a wireless LAN (local area network) interface, etc. Software anddata transferred via communications interface 924 are in the form ofsignals 928 which may be electronic, electromagnetic, optical, or othersignals capable of being received by communications interface 924. Thesesignals 928 are provided to communications interface 924 via acommunications path (i.e., channel) 926. This channel 926 carriessignals 928 and may be implemented using wire or cable, fiber optics, aphone line, a cellular phone link, a wireless link, and othercommunications channels.

[0103] In this document, the term “computer program product” refers toremovable storage units 918, 922, and signals 928. These computerprogram products are means for providing software to computer system900. The invention is directed to such computer program products.

[0104] Computer programs (also called computer control logic) are storedin main memory 905, and/or secondary memory 910 and/or in computerprogram products. Computer programs may also be received viacommunications interface 924. Such computer programs, when executed,enable the computer system 900 to perform the features of the presentinvention as discussed herein. In particular, the computer programs,when executed, enable the processor 903 to perform the features of thepresent invention. Accordingly, such computer programs representcontrollers of the computer system 900.

[0105] In an embodiment where the invention is implemented usingsoftware, the software may be stored in a computer program product andloaded into computer system 900 using removable storage drive 914, harddrive 912 or communications interface 924. The control logic (software),when executed by the processor 903, causes the processor 903 to performthe functions of the invention as described herein.

[0106] In another embodiment, the invention is implemented primarily inhardware using, for example, hardware components such as applicationspecific integrated circuits (ASICs). Implementation of hardware statemachine(s) so as to perform the functions described herein will beapparent to persons skilled in the relevant art(s).

[0107] In yet another embodiment, the invention is implemented using acombination of both hardware and software.

[0108] Conclusion

[0109] While various embodiments of the present invention have beendescribed above, it should be understood that they have been presentedby way of example only, and not limitation. It will be understood bythose skilled in the art that various changes in form and details maybemade therein without departing from the spirit and scope of theinvention as defined in the appended claims. Thus, the breadth and scopeof the present invention should not be limited by any of theabove-described exemplary embodiments, but should be defined only inaccordance with the following claims and their equivalents.

What is claimed is:
 1. A method for detecting spectral drift in ahyperspectral imaging system, comprising the steps of: (a) obtainingin-field measurements of a response function for a calibration filter;(b) obtaining in-field measurements of a response function for anonboard blackbody; (c) determining a spectral transmittance functionusing said response functions from steps (a) and (b) for saidcalibration filter and said onboard blackbody; (d) determining a firstderivative function of said spectral transmittance function; (e)separating said first derivative function into a plurality of spectralband regions, each of said spectral band regions having +/− N pixels oneither side of a localized minima; (f) determining a pixel shiftmagnitude value for one of said plurality of spectral band regions; and(g) applying said pixel shift magnitude value to a look-up table todetermine a magnitude and direction of said spectral drift for one ofsaid plurality of spectral band regions.
 2. The method of claim 1,wherein step (a) comprises the step of obtaining in field measurementsof a response function of a calibration filter, wherein said calibrationfilter is sequentially irradiated by first and second blackbody sources,respectively, wherein said first and second blackbody sources aremaintained at temperatures t₁ and t₂, respectively,
 3. The method ofclaim 2, wherein step (a) further comprises the step of obtainingmultiple frames of said response function of said calibration filtersequentially irradiated by said first blackbody source at temperature t₁and said second blackbody source at temperature t₂.
 4. The method ofclaim 1, wherein multiple frames of data are collected at equivalentframe times and ensemble averaged to obtain said response functions insteps (a) and (b).
 5. The method of claim 4, wherein step (c) furthercomprises the step of removing background radiance from said ensembleaveraged response functions to produce a spectral transmittancefunction.
 6. The method of claim 1, wherein step (b) comprises the stepof obtaining in-field measurements of said response function for saidonboard blackbody at temperatures t₁ and t₂, respectively.
 7. The methodof claim 1, wherein step (c) further comprises the step of normalizingsaid first derivative function of said spectral transmittance function.8. The method of claim 1, wherein said step of separating said firstderivative function into a plurality of spectral band regions enablesthe implementation of a full sensitivity to spectral drift, wherein thevalue of N varies with each of said spectral band regions.
 9. The methodof claim 1, wherein step (e) comprises the step of determining a sum ofthe differences between said first derivative function and a referencespectral derivative function from a starting point pixel number to anending point pixel number for one of said spectral band regions.
 10. Themethod of claim 1, further comprising the steps of: generating newspectral channel assignments for each pixel of said spectral band regionusing the spectral magnitude and direction of said spectral drift; andinterpolating values in between.
 11. The method of claim 1, furthercomprising the step of introducing said calibration filter sequentiallyirradiated by first and second blackbody sources into an optical path ofsaid hyperspectral imaging system using a flip mirror, prior toobtaining in-field measurements of said response function for saidcalibration filter.
 12. The method of claim 5, wherein step (c)comprises the steps of: determining a spectral difference function,wherein the spectral difference function is the difference between saidresponse function at temperature t₁ and said response function attemperature t₂; determining a blackbody difference function, wherein theblackbody difference function is the difference between said blackbodysource at temperature t₁ and said blackbody source at temperature t₂;and determining said spectral transmittance function, wherein saidspectral transmittance function is the quotient of the spectraldifference function and the blackbody difference function.
 13. Themethod of claim 1, wherein the value of N is selected to optimizedetection algorithm sensitivity to change while extending a limit ofspectral shift magnitude.
 14. The method of claim 1, wherein a spectralband per pixel for each spectral band region is defined by an opticalgeometry, a system focal length, a detector size, and a spectraldispersion rate design of said hyperspectral imaging system.
 15. Themethod of claim 1, wherein the generation of said reference derivativefunction comprises the steps of: (1) measuring multiple frames of areference spectrum of said calibration filter sequentially irradiated bysaid first and second blackbody sources in a laboratory environment; (2)measuring multiple frames of a reference spectrum of said first andsecond blackbody sources in a laboratory environment; (3) ensembleaveraging said reference spectrums from steps (1) and (2); (4) removingbackground radiance from said ensemble averaged reference functions toproduce a reference spectral transmittance function; and (5) determininga first derivative of said reference spectral transmittance function.16. The method of claim 15, wherein step (5) further comprises the stepof normalizing said first derivative of said reference spectraltransmittance function.
 17. The method of claim 1, further comprisingthe step of generating said look-up table from said first derivative ofsaid reference spectral transmittance function prior to performing step(g).
 18. The method of claim 17, wherein said step of generating saidlookup table comprises the steps of: (1) shifting said first derivativeof said reference spectral transmittance function by a predeterminedshift value in a positive and a negative direction to generate apositive and negative shifted derivative function; (2) determining thedifference between said positive and negative shifted first derivativefunction and said first derivative of said reference spectraltransmittance function to generate pixel shift magnitude values in saidpositive and negative direction, respectively; (3) storing said pixelshift magnitude values and the corresponding predetermined shift valuein said look-up table; and (4) repeating steps (1) through (3) usinganew predetermined shift value until said spectral band is covered. 19.The method of claim 18, further comprising the step of iterativelyrepeating steps (1) through (4) for a different spectral band until eachof said spectral bands is covered.
 20. A computer program productcomprising a computer useable medium having computer program logicrecorded thereon for enabling a computer to detect spectral drift in ahyperspectral imaging system, said computer program logic comprising:means for enabling a processor to obtain in-field measurements of aresponse function for a calibration filter; means for enabling aprocessor to obtain in-field measurements of a response function for anonboard blackbody; means for enabling a processor to determine aspectral transmittance function using said response functions for saidcalibration filter and said onboard blackbody; means for enabling aprocessor to determine a first derivative function of said spectraltransmittance function; means for enabling a processor to separate saidfirst derivative function into a plurality of spectral band regions,each of said spectral band regions having +/− N pixels on either side ofa localized minima; means for enabling a processor to determine a pixelshift magnitude value for one of said plurality of spectral bandregions; and means for enabling a processor to apply said pixel shiftmagnitude value to a look-up table to determine a magnitude anddirection of said spectral drift for one of said plurality of spectralband regions.
 21. The computer program product of claim 20, wherein saidmeans for enabling a processor to obtain in-field measurements of aresponse function for a calibration filter comprises means for enablinga processor to obtain in-field measurements of a response function for acalibration filter, wherein said calibration filter is sequentiallyirradiated by first and second blackbody sources, respectively, whereinsaid first and second blackbody sources are maintained at temperaturest₁ and t₂, respectively,
 22. The computer program product of claim 20,wherein said means for enabling a processor to obtain in-fieldmeasurements of a response function for a calibration filter furthercomprises means for enabling a processor to obtain multiple frames ofsaid response function of said calibration filter sequentiallyirradiated by said first blackbody source at temperature t₁ and saidsecond blackbody source at temperature t₂.
 23. The computer programproduct of claim 20, wherein multiple frames of data are collected atequivalent frame times and ensemble averaged to obtain said responsefunctions for said calibration filter and said onboard blackbody. 24.The computer program product of claim 23, wherein said means forenabling a processor to determine said spectral transmittance functionfurther comprises means for enabling a processor to remove backgroundradiance from said ensemble averaged response functions to produce saidspectral transmittance function.
 25. The computer program product ofclaim 20, wherein said means for enabling a processor to obtain in-fieldmeasurements of said response function for said onboard blackbodycomprises means for enabling a processor to obtain in-field measurementsof said response function for said onboard blackbody at temperatures t₁and t₂, respectively.
 26. The computer program product of claim 20,wherein said means for enabling a processor to determine said spectraltransmittance function further comprises means for enabling a processorto normalize said first derivative function of said spectraltransmittance function.
 27. The computer program product of claim 20,wherein said means for enabling a processor to separate said firstderivative function into said plurality of spectral band regions enablesthe implementation of a full sensitivity to spectral drift, wherein thevalue of N varies with each of said spectral band regions.
 28. Thecomputer program product of claim 20, wherein said means for enabling aprocessor to separate said first derivative function into said pluralityof spectral band regions comprises means for enabling a processor todetermine a sum of the differences between said first derivativefunction and a reference spectral derivative function from a startingpoint pixel number to an ending point pixel number for one of saidspectral band regions.
 29. The computer program product of claim 20,wherein said control logic further comprises: means for enabling aprocessor to generate new spectral channel assignments for each pixel ofsaid spectral band region using the spectral magnitude and direction ofsaid spectral drift; and means for enabling a processor to interpolatevalues in between.
 30. The computer program product of claim 20, whereinsaid control logic further comprises means for enabling a processor tointroduce said calibration filter sequentially irradiated by first andsecond blackbody sources into an optical path of said hyperspectralimaging system using a flip mirror, prior to obtaining in-fieldmeasurements of said response function for said calibration filter. 31.The computer program product of claim 24, wherein said wherein saidmeans for enabling a processor to determine said spectral transmittancefunction comprises: means for enabling a processor to determine aspectral difference function, wherein the spectral difference functionis the difference between said response function at temperature t₁ andsaid response function at temperature t₂; means for enabling a processorto determine a blackbody difference function, wherein the blackbodydifference function is the difference between said blackbody source attemperature t₁ and said blackbody source at temperature t₂; and meansfor enabling a processor to determine said spectral transmittancefunction, wherein said spectral transmittance function is the quotientof the spectral difference function and the blackbody differencefunction.
 32. The computer program product of claim 20, wherein thevalue of N is selected to optimize detection algorithm sensitivity tochange while extending a limit of spectral shift magnitude.
 33. Thecomputer program product of claim 20, wherein a spectral band per pixelfor each spectral band region is defined by an optical geometry, asystem focal length, a detector size, and a spectral dispersion ratedesign of said hyperspectral imaging system.
 34. The computer programproduct of claim 20, wherein the generation of said reference derivativefunction comprises: means for enabling a processor to measure multipleframes of a reference spectrum of said calibration filter sequentiallyirradiated by said first and second blackbody sources in a laboratoryenvironment; means for enabling a processor to measure multiple framesof a reference spectrum of said first and second blackbody sources in alaboratory environment; means for enabling a processor to ensembleaverage said reference spectrums from said calibration filter and saidfirst and second blackbody sources; means for enabling a processor toremove background radiance from said ensemble averaged referencefunctions to produce a reference spectral transmittance function; andmeans for enabling a processor to determine a first derivative of saidreference spectral transmittance function.
 35. The computer programproduct of claim 34, wherein said means for enabling a processor todetermine a first derivative of said reference spectral transmittancefunction further comprises means for enabling a processor to normalizesaid first derivative of said reference spectral transmittance function.36. The computer program product of claim 20, wherein said control logicfurther comprises means for enabling a processor to generate saidlook-up table from said first derivative of said reference spectraltransmittance function.
 37. The computer program product of claim 36,wherein said means for enabling a processor to generate said look-uptable comprises: shifting means for enabling a processor to shift saidfirst derivative of said reference spectral transmittance function by apredetermined shift value in a positive and a negative direction togenerate a positive and negative shifted derivative function;determining means for enabling a processor to determine the differencebetween said positive and negative shifted first derivative function andsaid first derivative of said reference spectral transmittance functionto generate pixel shift magnitude values in said positive and negativedirection, respectively; storing means for enabling a processor to storesaid pixel shift magnitude values and the corresponding predeterminedshift value in said lookup table; and repeating means for enabling aprocessor to repeat said shifting means through said storing means usinga new predetermined shift value until said spectral band is covered. 38.The computer program product of claim 37, wherein said control logicfurther comprises means for enabling a processor to iteratively repeatsaid shifting means through said repeating means for a differentspectral band until each of said spectral bands is covered.